If the function f(x)= cc 3 x-8, & if x 5 2 k, & if x>5 . is conti… - Vidyadip

MCQ

If the function $f(x)=\left\{\begin{array}{cc}3 x-8, & \text { if } x \leq 5 \\ 2 k, & \text { if } x>5\end{array}\right.$ is continuous, then the value of $k$ is

A
$2 / 7$
✓
$7 / 2$
C
$3 / 7$
D
$4 / 7$

✓

Answer

Correct option: B.

$7 / 2$

$\text { : Since } f(x) \text { is continuous at } x=5 \text {, }$
$\Rightarrow \lim _{x \rightarrow 5} f(x)=\lim _{x \rightarrow 5^{+}} f(x)=f(5)$
$\Rightarrow 3(5)-8=2 k$
$\Rightarrow 7=2 k$
$\Rightarrow k=\frac{7}{2}$

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